I think 4 is
Chechnya (The Chechen Republic) - they fought for independence in two Chechen wars, and they are a small region in the shadow of Russia
and 3 might be
Timor - currently split in East Timor and West Timor, divided by the Dutch and Portuguese in 1859, and it has quite a diverse population - according to Wikipedia, 11 different ethno-linguistic groups
1 might be
Nevis - a small island in the Caribbean Sea, part of the Federation of Saint Kitts and Nevis. Independence referendum held in 1998, with the majority voting for independence.
And 2 is maybe
Quebec - actively seeking independence from Canada, and has a long history of French influence/rule.
Edit:
For #2: My bad. Quebec is not larger than Mexico. I think Greenland (as explained by @1848) fits best.
Edit 2:
For 3, maybe a better fit would be
New Guinea - split to its eastern and western part, formerly a Dutch colony. From Wikipedia: "The island is presently populated by almost a thousand different tribal groups and a near-equivalent number of separate languages, which makes New Guinea the most linguistically diverse area in the world".